148 research outputs found
06391 Abstracts Collection -- Algorithms and Complexity for Continuous Problems
From 24.09.06 to 29.09.06, the Dagstuhl Seminar 06391 ``Algorithms and Complexity for Continuous Problems\u27\u27 was held
in the International Conference and Research Center (IBFI),
Schloss Dagstuhl.
During the seminar, participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar
are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
On the Robustness of Graph Neural Diffusion to Topology Perturbations
Neural diffusion on graphs is a novel class of graph neural networks that has
attracted increasing attention recently. The capability of graph neural partial
differential equations (PDEs) in addressing common hurdles of graph neural
networks (GNNs), such as the problems of over-smoothing and bottlenecks, has
been investigated but not their robustness to adversarial attacks. In this
work, we explore the robustness properties of graph neural PDEs. We empirically
demonstrate that graph neural PDEs are intrinsically more robust against
topology perturbation as compared to other GNNs. We provide insights into this
phenomenon by exploiting the stability of the heat semigroup under graph
topology perturbations. We discuss various graph diffusion operators and relate
them to existing graph neural PDEs. Furthermore, we propose a general graph
neural PDE framework based on which a new class of robust GNNs can be defined.
We verify that the new model achieves comparable state-of-the-art performance
on several benchmark datasets
Research and Education in Computational Science and Engineering
Over the past two decades the field of computational science and engineering
(CSE) has penetrated both basic and applied research in academia, industry, and
laboratories to advance discovery, optimize systems, support decision-makers,
and educate the scientific and engineering workforce. Informed by centuries of
theory and experiment, CSE performs computational experiments to answer
questions that neither theory nor experiment alone is equipped to answer. CSE
provides scientists and engineers of all persuasions with algorithmic
inventions and software systems that transcend disciplines and scales. Carried
on a wave of digital technology, CSE brings the power of parallelism to bear on
troves of data. Mathematics-based advanced computing has become a prevalent
means of discovery and innovation in essentially all areas of science,
engineering, technology, and society; and the CSE community is at the core of
this transformation. However, a combination of disruptive
developments---including the architectural complexity of extreme-scale
computing, the data revolution that engulfs the planet, and the specialization
required to follow the applications to new frontiers---is redefining the scope
and reach of the CSE endeavor. This report describes the rapid expansion of CSE
and the challenges to sustaining its bold advances. The report also presents
strategies and directions for CSE research and education for the next decade.Comment: Major revision, to appear in SIAM Revie
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